Musings at the bottom of a Mountain

by Pavan Kaushik – “ದೂರದ ಬೆಟ್ಟ ಕಣ್ಣಿಗೆ ನುಣ್ಣಗೆ”. This is a Kannada proverb which loosely translates to, a faraway hill appears calm, serene, devoid of thorns, bushes and imperfections. I think this summarises why so many adventure seeking individuals end up in a bad state and sometimes even death. Not clear? Here is my story. To understand it, we need to know why people die at all in these circumstances. Dehydration, fatigue and injuries are the primary causes. Why are these people ending up in such hapless states? It is more often than not because of error in their estimation of size and distance of their targets. Are these individuals naturally sloppy at distance estimation? Based on my personal observations the same individuals in a flat urban landscape are pretty good and judging distance. So why is it that these fit individuals end up in such perilous scenes? To answer this, one has to address the question of how one estimates distance.

Convergence: Due to our binocular vision, we have overlap in our visual field. Except they are from slightly different viewpoints. This angle difference(parallax) made by our eyes while looking at the object gives us an estimate its distance. The angle approaches 90° as the object approaches infinity. This is great in an ideal world but the real world has noise. There is a finite error in the estimation of angles. A conservative estimate of the error is about 0.1degrees. We can now see the problem. At small angles like 45, a 0.1 degree error corresponds to km error. But the same 0.1 degree error at 89 degrees corresponds to km error. One can easily misjudge distance in the order of kilometres except this argument is applicable to the urban scene.

Accommodation: Can we not judge distance with one eye? Yes we can. Close one of your eyes and keep your palm close to your open eye. Now move It slowly away. Do you “feel” something? It is the muscles around your lens which pushes and pulls the jelly mass to change its curvature which changes the focal length. This focal length decides what distances are in focus. The muscle strain is a proxy for distance except the same issue crops up. Beyond a particular distance the lens has no change in shape and thus giving you no clue of the distance. But this argument too is applicable to the urban context.

-from MKFI, Wikipedia.org

Familiar Size: Are these the only way we estimate absolute distance? This is when straight forward physics stops and biology kicks in. We use parallax, lighting, shadows, perspective, gradients, spectral decay and memory simultaneously to estimate distance. In the process we make some major assumptions about the world we live in. And these assumptions are the raw material for all the optical illusions. One classic example is the Ames room(wiki does an excellent job in explaining how it works). The famous illusion shows how heavily we rely on leading lines and perspective to estimate size and distance. Even after understanding how the illusion works, you can’t unsee the illusion, that is how deep our assumptions go in our brain. The illusion partly relies on we estimating sizes by familiarity. We have a memory yardstick, we know typically how large an apartment floor, a lamppost or a car is. Using this as a reference we can scale everything else around correspondingly. This is why most people are fair at distance estimation in the urban context. Cities are surrounded by parallel lines and well memorized objects for reference. Only when one encounters unknown terrain fun happens. We scan the new environment, look at objects, memorize their shape, patterns and typical sizes. For example, this could be nearby rocks and boulders. Now the adventurer feels confident about the place and thinks she/he can judge distances since they think they have a decent template map. They know the absolute distance of a nearby rock formation (using previous methods since it is not very far), and use it as a template to match with the target and they guesstimate the distance. This is when things go wrong. Look at the next few images and try to guess the distance.

Image #1

Image #2

Image #3

Image #1 is a 10 cm wide patch of fine silt. #2 is about a 20 cm borewell effluent. Image #3 is a roughly 5 m wide dried lake bed. Now you see what I’m talking about? Geological features look similar across scales and is a very common theme in physics. Since the underlying mechanisms of how water flows and soil mixing create repeatable fractal like patterns from glaciers, rivers eroding into a marsh to tiny streams gushing into land. Similarly the drying process causing cracks in materials can explain Continental plates , cracking of drought struck large land masses, clay on the lakebed, fine rock powder from borewell excavation to an idly. Google Earth of Himalayas would show you the recursiveness in geological formations. The patterns and textures on a pebble, Rock, boulder and a hillock look awfully similar so much so that one can’t distinguish them in an image. Except, the naive adventurer is ignorant of this fact that the patterns are recursive across scales. And when you template match a fractal there will be ambiguity, in the real world, this corresponds to grave errors in distance estimation. This is probably why I think many people end up making an error in the judgement of distance and lead to casualties.